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The variables m and n are positive integers. When m is divided by 18, [#permalink]
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28 Apr 2016, 01:15
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Re: The variables m and n are positive integers. When m is divided by 18, [#permalink]
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29 Apr 2016, 00:56
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m = 18k + 12 > Values are 12, 30, 48, 66, 84 n = 24k + 14 > Values are 14, 38, 62, 86
I. 50 > 12 + 38 > Possible II. 70 > Not possible III. 92 > 30 + 622 > Possible
Answer: D



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Re: The variables m and n are positive integers. When m is divided by 18, [#permalink]
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29 Apr 2016, 00:58
Bunuel wrote: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50 II. 70 III. 92
A. I only B. III only C. I and II D. I and III E. II and III m = 18x + 12 n = 24y + 14 m + n = 18x + 24y + 26 If x = 0 and y = 1, we have m + n = 0 + 24 + 26 = 50 If x = 1, y = 2, we have m + n = 18 + 48 + 26 = 92 Whatever values we try for x and y, m + n can never = 70 Correct Option: D



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Re: The variables m and n are positive integers. When m is divided by 18, [#permalink]
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02 Oct 2016, 08:16
m=18(k)+12 n=24(r)+14
Both m and n must also be a mulitiple of 6. Therefore on diving each by 6, remainder is 0 for m and 2 for n and m+n must give a remainder of 2 on division by 6. Thus only 50 and 92 fit the bill.



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Re: The variables m and n are positive integers. When m is divided by 18, [#permalink]
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02 Oct 2016, 09:22
deeksha6 wrote: m=18(k)+12 n=24(r)+14
Both m and n must also be a mulitiple of 6. Therefore on diving each by 6, remainder is 0 for m and 2 for n and m+n must give a remainder of 2 on division by 6. Thus only 50 and 92 fit the bill. Hi deeksha, You may be correct in your observation, but there is more to it.. If I give you say 14,20,32, they will fit in in your approach but will not be correct... Thus any of these choices used would have got you to a wrong answer Now WHY? m+n= 18a+24b+26... where m=18a+12 and n=24b+14... What Does 18a+24b+26 mean 1) it has to be more than 26.. 2) x and y will be integers so next number will be 26+18*1+24*0=26+18=44..m=12+18=30 and n=14.. Next 26+18*0+24*1=26+24=50..m is 12 and n 14+24=38 Next 26+18*2+24*0=26+36=62.. m is 12+18*2=48..n is 14 And so on
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Re: The variables m and n are positive integers. When m is divided by 18, [#permalink]
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01 Jan 2017, 11:28
m = 12, 30, 48, 66, .... n = 14, 38, 62, 86, ....... 12+38 = 50 30+62 = 92 Ans: D
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The variables m and n are positive integers. When m is divided by 18, [#permalink]
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01 Jan 2018, 11:01
m = 18p+12, n= 24q+14 m+n = 18p+24q+26 = 6(some quotient)+2, so choices should leave remainder when divided by 6 therefore answer is D) I ad III



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The variables m and n are positive integers. When m is divided by 18, [#permalink]
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01 Jan 2018, 19:01
Bunuel wrote: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50 II. 70 III. 92
A. I only B. III only C. I and II D. I and III E. II and III m+n=18q+24p+26 (m+n)/2=9q+12p+13 I. 2513=12=9q+12p possible: q=0; p=1 II. 3513=22=9q+12p not possible III. 4613=33=9q+12p possible: q=1; p=2 D



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The variables m and n are positive integers. When m is divided by 18, [#permalink]
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01 Jan 2018, 21:30
Bunuel wrote: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50 II. 70 III. 92
A. I only B. III only C. I and II D. I and III E. II and III (Divisor*quotient) + remainder = dividend 18*x + 12=m 24*w +14=n m+n= 18x+24w+26 for m+n =50, 50=18x+24w+26 This can be the case when w=1 and x=0. So possible for m+n=70 70=18x+24w+26. not possible for any combination of x and w. for m+n=92, 92=18x+24w+26 This can be the case when w=2 and x=1. so possible Hence D.
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Re: The variables m and n are positive integers. When m is divided by 18, [#permalink]
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02 Jan 2018, 00:41
Bunuel wrote: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50 II. 70 III. 92
A. I only B. III only C. I and II D. I and III E. II and III Think of it in terms of divisibility fundamentals " When m is divided by 18, there is a remainder of 12"  When m balls are divided into groups of 18, we are left with 12 balls "when n is divided by 24, there is a remainder of 14"  When n balls are divided into groups of 24, we are left with 14 balls So m + n balls would mean some groups of 18 balls, some groups of 24 balls and a group of 12+14 = 26 balls The groups of 18 balls can be split into 3 groups of 6 balls (HCF of 18 and 24) each and the groups of 24 balls can be split into 4 groups of 6 balls each too. As for the 26 balls, we can make 4 groups of 6 balls each and still have 2 balls leftover. So m + n would be 2 more than a multiple of 6. Only I and III satisfy this. Answer (D)
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